Soak the prunes in Armagnac overnight (or perhaps use preserved prunes in Armagnac from a gourmet shop, which have even more flavor because they'll have macerated longer). Drain, pit and roughly chop, reserving the liquid.
Melt 3 tablespoons of the butter in a saute pan and add the apples until soft, about 5 minutes. Sprinkle over 2 to 3 tablespoons of the sugar and continue cooking to caramelize, about 10 minutes more. Pour on about a tablespoon of the reserved Armagnac, flambe, and boil until the flames die out and the liquid has disappeared. Remove from the heat and taste. Depending on your apples, the mixture may need more acidity. If it does, add a squirt of lemon to taste. Stir through the chopped prunes.
Heat the oven to 375 degrees F/190 degrees C. Set the ring part of an 8-inch/20 cm springform pan on a baking sheet.
Prepare the pastry: Melt the remaining butter in a small saucepan or microwave. Working with one phyllo sheet at a time, prepare as follows: lay one sheet of phyllo on a clean surface and cut into three strips crosswise (not lengthwise). Brush one of the three strips with melted butter, sprinkle with a little sugar and a few drops of Armagnac. Lay another strip on top and repeat. Lay the final strip on top and brush with butter. Your single sheet of phyllo is now a three-layer-thick strip. Lay it in the center of the ring mold so that it runs from the middle out, and up and over the edge of the ring, like the spoke of a wheel. Continue with the remaining strips, laying them in around the ring slightly overlapping so that there are no openings.
Spoon the prune and apple filling into the bottom of the mold. Fold the pastry strips up in over top, twisting somewhat as you go so that the top is a rustic landscape of papery peaks and valleys totally covering the top of the tart. Brush quite generously with butter and scatter over a scant handful of sugar. (You may have some butter and sugar left over once you're done. If you do, use them for something else. The same goes for the Armagnac, of which you will have a lot left: use it in fruit salad or let a piece of pound cake drink it up...or serve it in tiny glasses with dessert.)
Remove the springform ring, leaving the formed croustade on the baking sheet. Bake until the pastry is fully cooked and golden, about 40 minutes. Remove from the oven, slide onto rack and cool. Serve with ice cream on the side or all on its own.